CF1876A.Helmets in Night Light

Pak Chanek is the chief of a village named Khuntien. On one night filled with lights, Pak Chanek has a sudden and important announcement that needs to be notified to all of the $n$ residents in Khuntien.

First, Pak Chanek shares the announcement directly to one or more residents with a cost of $p$ for each person. After that, the residents can share the announcement to other residents using a magical helmet-shaped device. However, there is a cost for using the helmet-shaped device. For each $i$, if the $i$-th resident has got the announcement at least once (either directly from Pak Chanek or from another resident), he/she can share the announcement to at most $a_i$ other residents with a cost of $b_i$ for each share.

If Pak Chanek can also control how the residents share the announcement to other residents, what is the minimum cost for Pak Chanek to notify all $n$ residents of Khuntien about the announcement?

帕克·查内克是名为昆田的村庄的村长。在一个灯火通明的夜晚，帕克·查内克有一项突发且重要的公告需要通知昆田村全部 $n$ 名居民。

首先，帕克·查内克可直接将公告告知一名或多名居民，每通知一人花费为 $p$。此后，居民们可借助一种魔法头盔状设备将公告传递给其他居民。然而，使用该头盔状设备需付出一定代价。对每个 $i$，若第 $i$ 位居民已至少一次获知该公告（无论是直接来自帕克·查内克，还是来自其他居民），则他/她最多可将公告传递给 $a_i$ 名其他居民，每次传递的花费为 $b_i$。

若帕克·查内克还可控制居民之间公告传递的具体方式，那么他通知昆田村全部 $n$ 名居民所需的最小总花费是多少？

Each test contains multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. The following lines contain the description of each test case.

The first line contains two integers $n$ and $p$ ($1 \leq n \leq 10^5$; $1 \leq p \leq 10^5$) — the number of residents and the cost for Pak Chanek to share the announcement directly to one resident.

The second line contains $n$ integers $a_1,a_2,a_3,\ldots,a_n$ ($1\leq a_i\leq10^5$) — the maximum number of residents that each resident can share the announcement to.

The third line contains $n$ integers $b_1,b_2,b_3,\ldots,b_n$ ($1\leq b_i\leq10^5$) — the cost for each resident to share the announcement to one other resident.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）—— 测试用例的数量。接下来的各行描述每个测试用例。

第一行包含两个整数 $n$ 和 $p$（$1 \leq n \leq 10^5$；$1 \leq p \leq 10^5$）—— 居民人数以及 Pak Chanek 直接向一名居民发布通知的成本。

第二行包含 $n$ 个整数 $a_1,a_2,a_3,\ldots,a_n$（$1\leq a_i\leq10^5$）—— 每名居民最多可将通知转发给的居民人数。

第三行包含 $n$ 个整数 $b_1,b_2,b_3,\ldots,b_n$（$1\leq b_i\leq10^5$）—— 每名居民将通知转发给另一名居民的成本。

保证所有测试用例中 $n$ 的总和不超过 $10^5$。

For each test case, output a line containing an integer representing the minimum cost to notify all $n$ residents of Khuntien about the announcement.

对于每个测试用例，输出一行，包含一个整数，表示通知坤田镇全部 $n$ 名居民该公告所需的最小花费。

In the first test case, the following is a possible optimal strategy:

1. Pak Chanek shares the announcement directly to the $3$-rd, $5$-th, and $6$-th resident. This requires a cost of $p+p+p=3+3+3=9$.
2. The $3$-rd resident shares the announcement to the $1$-st and $2$-nd resident. This requires a cost of $b_3+b_3=2+2=4$.
3. The $2$-nd resident shares the announcement to the $4$-th resident. This requires a cost of $b_2=3$.

The total cost is $9+4+3=16$. It can be shown that there is no other strategy with a smaller cost.

在第一个测试用例中，以下是一种可能的最优策略：

1. Pak Chanek 直接将公告分享给第 $3$、第 $5$ 和第 $6$ 位居民。这需要花费 $p+p+p=3+3+3=9$。
2. 第 $3$ 位居民将公告分享给第 $1$ 和第 $2$ 位居民。这需要花费 $b_3+b_3=2+2=4$。
3. 第 $2$ 位居民将公告分享给第 $4$ 位居民。这需要花费 $b_2=3$。

总花费为 $9+4+3=16$。可以证明，不存在花费更小的其他策略。